Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 7 - Applications of Trigonometry and Vectors - Section 7.4 Vectors, Operations, and the Dot Product - 7.4 Exercises - Page 329: 41

Answer

$123,155$

Work Step by Step

The formulas for horizontal component $x$ and vertical component $y$ of a vector $\textbf{v}$ having magnitude $|\textbf{v}|$ and direction angle $\theta$ are: $x=|\textbf{v}|\cos\theta$ and $y=|\textbf{v}|\sin\theta$ Substituting the values of $|\textbf{v}|=198$ and $\theta=128.5^{\circ}$ in the formulas above, $x=198\cos128.5^{\circ}\approx-123$ $y=198\sin128.5^{\circ}\approx155$ Therefore, $|\textbf{v}|=\langle -123,155 \rangle$ Since the question requires magnitudes of horizontal and vertical components, the magnitude of horizontal component is $123$ and the magnitude of vertical component is $155$.
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